On the condition number of the influence matrix belonging to some first kind integral equations with logarithmic kernel

Abstract

The solution of modified boundary integral equations of the first kind by using spline Galerkin or spline collocation yields corresponding discrete linear equations whose condition number increases with diminishing meshwidth. However, the condition number also depends on scaling of the unkowns and the equations. Based on the asymptotic error analysis for decreasing meshwidth we give estimates for the condition number which provide asymptotically optimal choices of the scalings in terms of the meshwidth